In a large bowl using a handheld mixer, whisk together the peanut butter and 1/2 cup heavy cream until light and fluffy and set aside. Make sure the whipping attachments are clean and then whip the remaining 2 cups cream with the sugar and vanilla until slightly stiff peaks form. Gently fold some of the whipped cream into the peanut butter mixture to lighten it up. Then add the peanut butter mixture back into the whipped cream in 3 parts, gently folding until combined, trying to keep it light and fluffy, and then set aside.
In a 9-inch springform pan, arrange a layer of cookies (about 16) overlapping in a circle, covering the entire surface. Spread a layer of whipped cream over the cookies, making sure all the cookies are covered, and top with banana slices. Repeat with the remaining cookies, whipped cream and banana slices, making 5 layers total and finishing with a layer of whipped cream on top. Cover with plastic wrap and refrigerate for at least 4 hours and up to overnight.
Cook's Note: Using a baby off-set spatula is a great tool to help smooth out the peanut butter whipped cream in your springform pan.